Four doughnuts and 4 coffees cost $12. The cost of the 4 coffees is half the cost of the 4 doughnuts. What is the cost of each c
1 answer:
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Answer:
The equation of the line is
Step-by-step explanation:
The general for of a line is:
(1)
where:
is the slope of the line and
is the intercept with the axis of the dependent variable,
in this case.
In order to obtain the value of the slope () we can use the corresponding slope formula:
(2)
where and
are the corresponding coordinates of the given points. In this case:
Substituting these values in equation (2) we obtain:
Hence, the line equation is now:
(3)
Now to obtain the value of you can follow two options:
- You can substitute one of your points,
or
, in equation (3). In this way, you will obtain an equation where the variable is
Note that for this question, it is easier to select point A because of having the independent variable equals to zero . Hence, substituting point A in equation (3):
Therefore, the line equation is:
The second option to find is to think of the meaning of the <em>intercept</em>. The <em>intercept </em>of a line is defined as the point in which the line crosses the axis of the dependent variable, which also means that the value of the independent variable for this point is zero. From this, we could have automatically said that
is equal to
.
See the attachment for a plot of the line.
Answer:
D. 0.9953 (Probability of a Type II error), 0.0047 (Power of the test)
Step-by-step explanation:
Let's first remember that a Type II error is to NOT reject H0 when it is false, and the probability of that occurring is known as β. On the other hand, power refers to the probability of rejecting H0 when it is false, so it can be calculated as 1 - β.
To resolve this we are going to use the Z-statistic:
Z = (X¯ - μ0) / (σ/√n)
where μ0 = 1.2
σ = 5
n = 42
As we can see in part A of the attached image, we have the normal distribution curve representation for this test, and because this is a two-tailed test, we split the significance level of α=0.01 evenly into the two tails, 0.005 in each tail, and if we look for the Z critical value for those values in a standard distribution Z table we will find that that value is 2.576.
Now we need to stablish the equation that will telll us for what values of X¯ will we reject H0.
Reject if:
Z ≤ -2.576 Z ≥ 2.576
We know the equation for the Z-statistic, so we can substitute like follows and resolve.
Reject if:
(X¯ - 1.2) / (5/√42) ≤ -2.576 (X¯ - 1.2) / (5/√42) ≥ 2.576
X¯ ≤ -0.79 X¯ ≥ 3.19
We have the information that the true population mean is 1.25, so we now for a fact that H0 is false, so with this we can calculate the probability of a Type II error: P(Do not reject H0 | μ=1.25)
As we can see in part B of the attached image, we can stablish that the type II error will represent the probability of the sample mean (X¯) falling between -0.79 and 3.19 when μ=1.25, and that represents the shaded area. So now we now that we are looking for P(-0.79 < X¯ < 3.19 | μ=1.25).
Because we know the equation of Z, we are going to standardize this as follows:
P ( (-0.79 - 1.25) / (5/√42) < Z < (3.19 - 1.25) / (5/√42) )
This equals to:
P(-2.64 < Z < 2.51)
If we go and look for the area under the curve for Z positive scores in a normal standart table (part C of attached image), we will find that that area is 0.9940, which represents the probability of a Type II error.
Therefore, the power of the test will be 1-0.9940 = 0.006
If we look at the options of answers we have, there is no option that looks like this results, which means there was a probable redaction error, so we are going to stay with the closest option to these values which is option D.
